Grouping of multi-dimensional observations with the vehicle rotation model: Application of assigning the students to dorm rooms by personal inventory

In our study, the vehicle routing problem model has been modified to cluster the multi-dimensional observations as optimum solution. The classical vehicle routing problem model can perform intuitive clustering when start point definition is disabled. Vehicle routing in order to become a model of producing definitive solution, we define a diagonal length variable for the closed-end routes and we integrated the model. The most important difference of the output of the model we have developed from the outputs of the clustering analysis is that the user can determine the element numbers of the subclasses to be generated. In order to test the model we developed, we solved our model by using software that performs integer linear programming. We also compared the results with the same data, the method of evaluating all the alternatives giving the definitive solution, and the results. In repetitive tests, one-to-one correspondence has been achieved between the outputs of two different methods and our tests have been successful. We tested the modeling effect of different distance function outputs. Using the same data matrices, the distance matrices obtained from different distance functions were solved together with our model and the results were compared. The distance functions which do not take into account the inter-criteria interactions gave the same results in themselves, similarly the distance functions taking into account the inter-criteria interactions gave the same results in themselves. In order to apply the model we developed, we obtained a data matrix from the students who stayed in the student's residence with our five-factor model subscale and some additional criteria. Data matrices were transformed into distance matrices with the aid of distance functions. The distance matrices have been solved together with the modified vehicle routing model we have developed. Thus, students with similar personality inventory were clustered in the same room.